Raising and lowering operators for Askey-Wilson polynomials

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Abstract

In this paper we describe two pairs of raising/lowering operators for Askey- Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the "classical" properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

Original languageEnglish (US)
Article number002
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume3
DOIs
StatePublished - Jan 1 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Keywords

  • Askey-Wilson polynomials
  • Double affine Hecke algebra
  • Lowering operators
  • Orthogonal polynomials
  • Raising operators
  • Root systems
  • Three term recurrence
  • q-difference equation

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